A and B are two identical balls attached to strings as...

A and $B$ are two identical balls attached to strings as shown. A is released from position OA. A collides with B elastically. Then, (a) $\mathrm{A}$ and $\mathrm{B}$ move with different non-zero velocities (b) $\mathrm{B}$ moves forward and $\mathrm{A}$ rebounds with the same velocity (c) A and B stick together and move with same velocity (d) A comes to rest and $B$ moves with the velocity of $A$

A and $B$ are two identical balls attached to strings as shown. A is released from position OA. A collides with B elastically. Then,
(a) $\mathrm{A}$ and $\mathrm{B}$ move with different non-zero velocities
(b) $\mathrm{B}$ moves forward and $\mathrm{A}$ rebounds with the same velocity
(c) A and B stick together and move with same velocity
(d) A comes to rest and $B$ moves with the velocity of $A$

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Key Concepts

Elastic Collision

An elastic collision is one in which both momentum and kinetic energy are conserved. In such collisions, no energy is lost to sound, heat, or deformation, allowing for precise predictions about the post-collision speeds of the objects involved.

Conservation of Momentum

The conservation of momentum principle states that the total momentum of an isolated system remains constant before and after a collision. This concept is crucial in analyzing collisions, as it provides a relationship between the velocities and masses of the colliding objects.

Conservation of Kinetic Energy

In elastic collisions, kinetic energy is conserved along with momentum. This allows for the simultaneous use of both conservation laws to determine the final velocities of the colliding bodies, ensuring that the energy present before the collision is equal to the energy after the collision.

Collisions Involving Identical Masses

When identical masses are involved in an elastic collision, the analysis becomes straightforward because the mass terms cancel out in the conservation equations. A common result in such cases is that the moving object transfers its velocity to the initially stationary one, often leaving the moving object at rest after the collision.

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